Rotational Distributions and Imaging of Singlet O2 Following Spin-Forbidden Photodissociation of O3

We report REMPI spectra and velocity-mapped ion images of the O2(a1Δg) and (b1Σg+) fragments arising from the spin-forbidden photodissociation of O3 near 320 and 330 nm. The O2(a1Δg, v = 0) REMPI spectrum following a 320 nm dissociation shows enhanced peak intensity for the odd rotational states relative to the even states, which is the opposite of the trend observed by Gunthardt et al. (J. Chem. Phys.2019, 151, 22430231837678 ) for spin-allowed dissociation at 266 nm but is consistent with the couplings between the B state and 3A′ and 3A″ states calculated by Grebenshchikov and Rosenwaks (J. Phys. Chem. A2010, 114, 9809–981920509638 ). There are no significant differences between the ion image angular distributions of fragments in odd and even rotational states, which indicates a cold distribution of O3 and supports the explanation that the alternation in peak intensities results from a difference in the couplings. Quantitative analysis of the image angular distributions was limited due to the single laser polarization geometry accessible in one-color experiments. Radial distributions of the 320 nm images indicate a broad rotational distribution, evidenced in bimodal speed distributions with peaks corresponding to both high (j = 35–43) and low (j = 17–20) rotational states. The REMPI spectrum of O2(a1Δg) near 330 nm was collected, and while quantitative population analysis is difficult because of the perturbed resonant state, the spectrum clearly supports a broad rotational distribution as well, consistent with the images collected at 320 nm. A 2D-REMPI spectrum was collected following dissociation of O3 near 330 nm, which showed evidence of contributions from O2 fragments in both the a1Δg and b1Σg+ states. The rotational distribution for the O2(b1Σg+, v = 0) product peaks at j = 32 and is narrower than that of the O2(a1Δg) fragment, consistent with distributions reported by O’Keeffe et al. at longer dissociation wavelengths (J. Chem. Phys.2002, 117, 8705–8709). At smaller radii in the 2D-REMPI spectrum, there is additional signal assigned to v = 1–4 of O2(b1Σg+), with rotational distributions similar to v = 0. The vibrational distribution of the O2(b1Σg+) fragment peaks at v = 0, with populations monotonically decreasing with increasing vibrational state. Ion image angular distributions of the O2(b1Σg+) fragment and the corresponding anisotropy parameters are also reported.


INTRODUCTION
−37 Absorption in both bands is due to transitions from ground state, O 3 (X 1 A′), to the B state (3 1 A′).In the Hartley band, excitation occurs to the continuum of the B state above the dissociation threshold, and the absorption spectrum is broad, peaking near 260 nm.−43 Both O( 1 D) and O 2 (a 1 Δ g ) have been observed at dissociation wavelengths longer than 310 nm, despite the spin-allowed singlet channel being energetically inaccessible.3][4][5]24 In the Hartley and Huggins bands, there are five energetically accessible dissociation channels, where channels 1 and 5 are spin-allowed and channels 2−4 are spin-forbidden following initial excitation to the B state.
Studies of the O( 3 P) fragment following photodissociation in the Huggins band reported branching ratios of channels 3−5 to be approximately equal, 4,6 and studies of the O( 1 D) fragment at long dissociation wavelengths have indicated a yield of 0.1. 7,17Thus, spin-forbidden processes are significant sources of excited O and O 2 products in the Huggins band.
The spin-allowed channels 1 and 5 have been studied extensively following Hartley band dissociation both experimentally and theoretically.In the triplet channel (5), the O 2 (X 3 Σ g − ) products are highly vibrationally and rotationally excited, and the vibrational distribution is strongly dependent on wavelength, with increasing vibrational excitation at shorter dissociation wavelengths. 8,9The spatial anisotropy (β) in the triplet channel varies with the rotational state as a result of bending motion at the time of dissociation, with positive β values at low rotational states and negative β values at high rotational states.−10 The rotational state distribution shifts to higher rotational states with higher-energy dissociations, and calculated distributions for this channel match experimental distributions. 8,19,30,31For all wavelengths, the singlet channel β is positive, increasing with longer dissociation wavelengths as a result of the restoring force in the bending potential, which more strongly affects fragments with slower recoil velocity. 8,31,32he rotational distribution of the singlet channel O 2 (a 1 Δ g ) has been of particular interest because of the observed alternation of odd and even rotational states, 19,30 which is attributed to a Λ-doublet propensity that leads to a preference for even rotational states. 11,30,33A nonrotating O 3 molecule has A′ symmetry with respect to the molecular plane, so there is a preference to conserve symmetry and form the O 2 A′ Λdoublet, which must correspond to even rotational states due to symmetry restrictions.This alternation is highly temperature-dependent.There are three rotation axes in ozone: one axis is perpendicular to the molecular plane and two are in the molecular plane, and the final fragment angular momentum has components along all three axes.At higher temperatures, rotation about the two in-plane axes results in a rotation of the molecular plane and tilts the fragment O 2 rotation plane relative to the initial plane.This breaks the symmetry restrictions and allows mixing of the A′ and A″ Λ-doublets.This results in a greater population of odd rotational states of O 2 .The angular distributions of the O 2 ion images in odd and even rotational states also support the idea that odd j-state fragments originate from warmer parent distributions, with weaker correlations between the fragment velocity v and angular momentum j vectors as well as the transition dipole moment μ and j vectors in odd rotational states.The v and j vectors are expected to be perpendicular in the dissociation of a triatomic molecule, but greater out-of-plane rotation of the parent molecule decreases the angle between v and j.
There have been far fewer dynamics studies involving Huggins band dissociation of O 3 below the energetic threshold for the spin-allowed singlet channel.Absorption in the Huggins band is much weaker than the Hartley band due to a large difference between the X and B equilibrium geometries and exhibits vibronic structure.Figure 1 shows potential energy curves calculated by Grebenshchikov and Rosenwaks for a fixed bond length of the second O−O bond (2.43 a 0 ) and bond angle (117°). 12The X, B, and R states are all 1 A′ and are shown in black.These three states account for all of the observed dynamics in Hartley band dissociations.In the Huggins band, initial excitation is to the bound region of the B state, but only triplet states correlate to spin-forbidden products.The triplet states that cross the B state and lead to spin-forbidden products are shown in Figure 1 in blue.Following initial excitation to the bound region of the B state, there are pathways involving both 3 A′ states (solid lines) and 3 A″ states (dashed lines) that cross the minimum of the B state and correlate with spin-forbidden products.The relative importance of interactions between the B state and the 3 A′ and 3 A″ states in spin-forbidden processes have not been well characterized, but Grebenshchikov and Rosenwaks calculated couplings between the B state and each of the 3 A′ and 3 A″ states for a single geometry. 12n addition to the measurement of the O( 3 P 0 ) fragment translational energy suggesting equal branching between channels 3−5, 4 REMPI spectra of the b 1 Σ g + state were collected by O'Keeffe et al. 13,34 The b 1 Σ g + state REMPI was fit to obtain rotational state distributions, which O'Keeffe et al. reported peaked at j = 28 for a 344 nm dissociation and j = 34 for a 337.2 nm dissociation.More recently, Ulrich et al. collected ion images of O( 3 P 2 ) following dissociation between 321 and 329 nm. 6The speed distributions of these images were fit to estimate the vibrational state distributions of each of the three channels, assuming a single rotational temperature for all three The Journal of Physical Chemistry A electronic states of O 2 .However, the unresolved nature of the derived speed distributions, due to the large number of possible coincident O 2 fragment states, precludes quantitative analysis.Measuring the O 2 (a 1 Δ g ) or O 2 (b 1 Σ g + ) molecular fragments directly provides an opportunity to gain additional insight into the dissociation dynamics by resolving the rotational and vibrational distribution of the O 2 fragment.Ulrich et al. also reported spatial anisotropy values for the O( 3 P 2 ) images, with β ranging from −0.59 to 2.00 for individual features in the images assigned to O( 3 P 2 ) formed with O 2 in the X 3 Σ g − , a 1 Δ g , or b 1 Σ g + states.Since the assignment of peaks in the radial distributions of these images is difficult, the wavelength dependence of β in each of the channels (3−5) is unclear.Images of the O 2 fragment would complement the O( 3 P 2 ) images, and obtaining β values from the O 2 images would provide valuable information on individual dissociation channels and facilitate comparison to theory.

EXPERIMENTAL SECTION
The molecular beam/velocity map ion imaging apparatus has previously been described. 44,45The O 3 molecular beam was generated by flowing He over O 3 trapped on silica beads at −40 °C for a total pressure of 800 Torr, expanded through a General Valve series 9 pulse valve and collimated by a 1 mm conical skimmer.The molecular beam was intersected at 90°b y a linearly polarized laser beam generated by frequency doubling the output of a dye laser (LAS LDL 2051) operating at 640−660 nm, pumped by a frequency-doubled Spectra Physics LAB 150−10 Nd:YAG laser.The wavelength of the laser was calibrated by optogalvanic spectroscopy, using a Mg− Ne or Cu−Ne hollow cathode lamp.The O 2 fragments were probed using 2 + 1 Resonance-Enhanced Multiphoton Ionization (REMPI) via the d 1 Π g state.The lower vibrational states (v = 0−3) of the d 1 Π g state are perturbed by the nearby II 1 Π g valence state and therefore are not ideal for extracting accurate rotational state distributions, but v ≥ 4 lie above the dissociation threshold of the II 1 Π g state, are unperturbed, and therefore can be used to obtain rotational state information.The 2−0 band of the O 2 (d 1 Π g ←← a 1 Δ g ) transition at 320 nm was used for O 2 (a 1 Δ g ) ion images and a REMPI spectrum for comparison to the 266 nm dissociation study of Gunthardt et al. 11 A 2D-REMPI spectrum 46−49 was collected near 330 nm in which images were obtained at each wavelength step and the reconstructed radial distributions were plotted as a function of wavelength.330 nm corresponds to the 4−0 band of the O 2 (d 1 Π g ←← b 1 Σ g + ) transition and the 1−0 band of the O 2 (d 1 Π g ←← a 1 Δ g ) transition.Wavelengths near 330 nm were used to measure the rotational and vibrational state distributions of the O 2 (b 1 Σ g + ) fragment, as well as to collect ion images.The rotational distribution of O 2 (a 1 Δ g , v = 0) at 330 nm is also discussed.
Following ionization, the O 2 cations were accelerated by velocity mapping electrostatic lenses down a 50 cm field-free flight tube coaxial with the molecular beam and projected onto a position-sensitive detector composed of microchannel plates gated to selectively detect the mass of interest and a phosphor screen.The resulting images were collected by a CCD camera.For the 1D rotational spectra, a mask was used to block the low-velocity fragments and nonresonant signal in the O 2 (d 1 Π g , v = 2 ←← a 1 Δ g , v = 0) REMPI spectrum at 320 nm and the center spot in the O 2 (d 1 Π g , v = 1 ←← a 1 Δ g , v = 0) REMPI spectra at 330 nm, and the signal of interest was collected using a photomultiplier tube (PMT).
Typical laser energies were 4−5 mJ for the 320 nm 1D-REMPI, 6−8 mJ for the 330 nm 1D-REMPI, and 9−10 mJ for the 330 nm 2D-REMPI.All experiments were one-color experiments, using a vertically polarized laser (parallel to the imaging plane).The polarization of the laser was controlled with a photoelastic modulator and a Glan polarizer.
The beam temperature was estimated by NO calibration.A molecular beam of NO in He was used with seeding similar to that of a typical O 3 beam, and the same pulse valve timing was used.NO was probed using the A ← X transition via 1 + 1 REMPI at 226 nm.The 226 nm laser had 50−100 μJ of power, and the ion optics were defocused to spread out the NO signal from the center of the image.The NO REMPI spectrum was fit with LIFBASE to obtain a beam temperature of 50 K. 50The spectrum and fit are shown in the Supporting Information.

RESULTS AND DISCUSSION
3.1.Photodissociation near 320 nm.3.1.1.Even−Odd Alternation in the O 2 (a 1 Δ g ) Fragment.For photodissociation at 320 nm, the spin-allowed dissociation channel producing O 2 (a 1 Δ g ) and O( 1 D) is not energetically accessible from cold parent molecules.In one-color images of the O 2 (a 1 Δ g ) fragments following 320 nm dissociation of O 3 , two regions of resonant signal were observed: a sharp outer ring at large radii and a broader ring at smaller radii (vide infra).The signal at smaller radii, corresponding to slower fragment velocities, is due to spin-allowed dissociation via channel 1 originating from vibrationally excited O 3 .The low-velocity signal was blocked with a mask and, therefore, does not contribute to the REMPI spectrum shown in Figure 2. The outer ring corresponds to spin-forbidden dissociation producing O 2 (a 1 Δ g ) and O( 3 P) (channel 4) based on analysis of the derived speed distribution.
Figure 2 shows a comparison of the O 2 (d 1 Π g , v = 2 ←← a 1 Δ g , v = 0) REMPI spectrum following 320 nm dissociation (top) in a one-color experiment and the spectrum reported by Gunthardt et al. 11 following a 266 nm dissociation (bottom).The peaks correspond to the S-branch transitions of rotational states j = 16−20.There is an overlap with the P-branch j = 42 transition in the 320 nm spectrum (indicated by an asterisk).Hartley band dissociation of O 3 at 266 nm with a rotational 0) transition.The bottom spectrum was collected following dissociation at 266 nm 11 and the top spectrum near 320 nm in a onecolor experiment.S-branch transitions are indicated by the comb at the top, and the peak marked by an asterisk corresponds to the overlapping P-branch j = 42 transition.
The Journal of Physical Chemistry A temperature of 100 K shows significant suppression of the odd rotational states of O 2 , which results from a Λ-doublet propensity in which the A′ Λ-doublet is primarily formed to conserve the A′ symmetry of the parent O 3 .Due to symmetry restrictions, the A′ Λ-doublet leads to even rotational states of O 2 and the A″ Λ-doublet leads to odd rotational states; therefore, the preference for the A′ Λ-doublet leads to a preference for even rotational states of O 2 (a 1 Δ g ).The Λdoublet propensity and the resulting alternation between the even and odd rotational states are highly temperaturedependent since the out-of-plane rotation of the parent O 3 mixes the Λ-doublets.As a result, there is a greater population of odd rotational states and less alternation between the even and odd rotational states following dissociation of a warmer parent rotational distribution.
While the peaks corresponding to odd rotational states are highly suppressed following a 266 nm dissociation, the odd peaks are clearly enhanced following a 320 nm dissociation, despite the colder beam temperature of 50 K.Although quantitative rotational state populations cannot be obtained from the 2−0 band of the d 1 Π g ←← a 1 Δ g transition because of the highly perturbed nature of the low vibrational states of the O 2 (d 1 Π g ) state, a comparison of the two spectra shown in Figure 2 suggests a fundamental difference between dissociation at 320 and 266 nm.We believe this is due to greater coupling between the B state and repulsive 3 A″ states relative to the coupling between the B state and 3 A′ states leading to O( 3 P) and O 2 (a 1 Δ g ) products. 12,35Grebenshchikov and Rosenwaks calculated spin−orbit matrix elements between the B state and the repulsive 3 A′ and 3 A″ states producing spinforbidden products for a single geometry (R 1 = 2.43 a 0 , R 2 = 3.20 a 0 , α = 117°) and found stronger coupling between the B state and the 3 A″ repulsive states which would lead to odd rotational states of O 2 , consistent with experiment. 12The relative probabilities of transitions from the B state to 3 A″ states compared to transitions from the B state to 3 A′ states can be estimated with a 1D Landau−Zener model, where P is the probability of transition, Δ T is the spin−orbit matrix element between the B and triplet states, ν is the relative velocity, and F B and F T are the slopes of the B and triplet state potentials at the crossing point, respectively.The probability was calculated for each triplet state with its corresponding spin−orbit matrix element from Grebenshchikov and Rosenwaks, reflecting the coupling of the triplet state to the B state.Summing the probabilities of transition to each of the individual 3 A′ and 3 A″ triplet states that correlate with the O 2 (a 1 Δ g ) and O( 3 P) fragments approximates the overall probability of transitions to 3 A′ versus 3 A″ states, which corresponds to the relative probability of forming even and odd rotational states, respectively.As discussed previously, the O 2 states with A′ symmetry must correspond to even rotational states and the states with A″ symmetry must correspond to odd.The O 2 (a 1 Δ g ) fragment was previously shown to conserve the symmetry of the parent O 3 following Hartley band dissociation at cold temperatures, 11,33 so the ratio of even and odd rotational states of O 2 (a 1 Δ g ) should reflect the crossing probability of the parent O 3 to 3 A′ and 3 A″ states.Using the Landau−Zener model for a 320 nm dissociation and couplings from Grebenshchikov and Rosenwaks, the overall probability of transitions from the B state to 3 A″ state is predicted to be 1.55 times higher than transitions from the B state to 3 A′ state for the geometry used in the calculations, which would result in increased populations of odd rotational states.Additional details about the calculations are included in the Supporting Information.The intensity of the even and odd transitions in the 320 nm REMPI spectrum indicate that both A′ and A″ states contribute to the formation of O 2 (a 1 Δ g ) products, and the A″ states dominate.Despite the simplicity of this analysis, it provides a very reasonable agreement with the observed enhancement of the odd peaks in the 320 nm spectrum in Figure 2 relative to the 266 nm spectrum.
Ion images can be used to further study dissociation dynamics through fitting the angular distributions to obtain vector correlations between the parent transition dipole moment μ, the fragment velocity v, and the fragment angular momentum j, which provide information about the dynamics of the dissociation.In the Hartley band, differences in the vector correlations between the even and odd rotational states of O 2 (a 1 Δ g ) support the Λ-doublet model. 11In a typical twocolor experiment, images are collected in three geometries (VV, HV, and VH, where V and H indicate polarization of the photolysis and probe lasers parallel and perpendicular to the imaging plane, respectively), and the angular distributions of each image are fit to obtain bipolar moments using the equations of Wei et al. 51 Following the semiclassical bipolar moment formalism of Dixon, the low-order bipolar moments β 0 2 (20), β 0 0 (22), and β 0 2 (02) represent the expectation value of the second Legendre polynomial ⟨P 2 (cos θ)⟩ where θ is the angle between the μ − v, v − j, and μ − j vectors, respectively. 52According to this formalism, the bipolar moment will be −0.5 if the vectors are perpendicular, and 1 if the vectors are parallel.The well-known spatial anisotropy parameter β is related to β 0 2 (20) by the relation β = 2β 0 2 (20).Image angular distributions are reported in terms of the image anisotropy parameters β 2 and β 4 rather than β 0 2 (20), β 0 0 (22), and β 0 2 (02) because of the limitations of the vector correlation analysis possible in a one-color experiment.The reported values of β 2 and β 4 are related to the bipolar moments through the equations of Wei et al. 51 Figure 3 shows ion images of O 2 (a 1 Δ g ) in j = 19 and 20 following dissociation of O 3 near 320 nm.These images were collected in a single laser experiment with vertical polarization at wavelengths corresponding to the R-and S-branch transitions of j = 19 and 20.As discussed above, the outermost ring in the images corresponds to the highest fragment speed, associated with the spin-forbidden dissociation channel (4).The signal in the image at radii less than half the outer ring is associated with spin-allowed dissociation of vibrationally excited O 3 based on its translational energy.The signal at intermediate radii corresponding to approximately half the speed of the outer ring is diffuse, nonresonant, and is largely independent of wavelength.Images were symmetrized and reconstructed, and a narrow radial range of the outer ring was integrated to obtain the angular distributions shown on the right in Figure 3.The experimental angular distributions are shown in black circles, and the red line is fit to the equation to obtain the image anisotropy parameters, β 2 and β 4 , where I(θ) is the angle-dependent intensity and P 2 and P 4 are the second and fourth Legendre polynomials, respectively.The values of β 2 and β 4 are reported in Table 1.

The Journal of Physical Chemistry A
The intensity at the top and bottom of the images and the positive β 2 values are indicative of a parallel transition, as expected for transition to the B state of O 3 .Because excitation in both the Hartley and Huggins bands is a parallel transition to the B state, the μ-v correlation should be positive.The outer rings in the S-branch images show 2-fold symmetry, and the Rbranch images show 4-fold symmetry, consistent with a perpendicular v-j correlation and expected for a triatomic dissociation.Following 266 nm dissociation, the anisotropy parameters and corresponding vector correlations are similar for odd and even rotational states at low temperatures but differ significantly at warmer temperatures. 11The values of β 0 0 (22) and β 0 2 (02) for j = 19 are closer to zero at higher temperatures due to greater depolarization of the v-j and μ-j correlations because the odd rotational states of O 2 originate from warmer parent molecules with greater angular momentum.Increased out-of-plane rotation decreases the angle between v and j.Although the differences are more significant at higher temperatures, differences between β 0 0 (22) and β 0 2 (02) for even and odd rotational states can be seen across a range of temperatures.
Complete analysis of the 320 nm image anisotropy parameters to extract vector correlations is not possible because the images were limited to a single geometry, but the similarity between the angular distributions and image anisotropy parameters of odd and even rotational states is indicative of a cold molecular beam, consistent with the NO calibration previously discussed.This supports the explanation that the increased intensity of the odd rotational peaks in Figure 2 is a result of differences in 3 A′ and 3 A″ coupling to the B state rather than a depolarization mechanism from a warmer distribution of O 3 .Furthermore, given the hypothesis that the even and odd states originate from dissociation along the 3 A′ and 3 A″ repulsive states, respectively, the results imply similar dynamics on these surfaces, as expected.
3.1.2.O 2 (a 1 Δ g , v = 0) Rotational Distribution at 320 nm.The 2−0 band of the O 2 (d 1 Π g ←← a 1 Δ g ) transition was previously measured by Gunthardt et al. to study the temperature-dependent alternation between odd and even rotational states of O 2 following a 266 nm dissociation since the perturbed 2−0 transition exhibited more intense peaks corresponding to odd rotational states than unperturbed vibrational bands. 11Although the perturbations limit the use of the 2−0 REMPI spectrum to obtain accurate rotational state populations, we find strong evidence to suggest that the O 2 (a 1 Δ g ) rotational distribution at 320 nm is broader than that at 266 nm.Han et al. employed the unperturbed 4−0 band instead to obtain the rotational state distribution of O 2 (a 1 Δ g ) following O 3 dissociation at 266 nm and found population in rotational states ranging from j = 13 to j = 37. 33 The perturbations in the 2−0 band lead to several overlapping peaks in the REMPI spectrum that correspond to a combination of a low j and high j states from different branches which have been assigned by Morrill et al. 53 Although the R and S branches for j = 15−21 in the 2−0 spectrum are overlapped by transitions from j = 35 to j = 44, these states are not observed following 266 nm dissociation, consistent with their low populations and confirmed by the unimodality of the speed distributions. 11At 320 nm, however, the speed distributions in this region are multimodal, indicating contributions from fragments at multiple speeds.Figure 4 shows the outer edge of reconstructed images of O 2 (a 1 Δ g ) following a 320 nm dissociation of O 3 at wavelengths   The Journal of Physical Chemistry A corresponding to S-and R-branch transitions of j = 17 and j = 20.While there is a single outer ring in the j = 20 images, the ring is split in the j = 17 images, indicative of overlapping transitions from different O 2 (a 1 Δ g ) rotational states.
Figure 5 shows the speed distributions derived from the reconstructed images in Figure 4.The speed distributions for j = 20 in both the S and R branches are unimodal, consistent with the distributions observed at 266 nm by Gunthardt et al. 11 and indicative of a single rotational transition.In contrast, the speed distributions for j = 17 in both the S and R branches show additional contributions from slower fragments, indicating the presence of higher rotational states.The difference in energy of the fragments is consistent with the j = 35 (Pbranch) and j = 43 (O-branch) transitions overlapping with the j = 17 (S-branch) transition and the j = 39 (P-branch) transition overlapping with the j = 17 (R-branch) transition, which are predicted based on the assignments of Morrill et al. 53 The primary source of broadening in the speed distributions is instrumental uncertainty, and the speed distributions have been fit with Gaussian distributions with σ = 40 m/s, centered at the expected speeds based on the fragment rotational states.Additional images and speed distributions for j = 18 and 19 are included in the Supporting Information and also show evidence for j > 30 rotational states.
The fragment rotational distribution is a function of both the available energy and the dynamics of the dissociation, and while quantitative rotational state populations cannot be obtained from the O 2 (d 1 Π g , v = 2 ←← a 1 Δ g , v = 0) REMPI spectrum and images, it is clear that higher rotational states are populated following a 320 nm spin-forbidden dissociation than observed following a 266 nm spin-allowed dissociation.Additional direct evidence for the population of high rotational states is seen in the S-branch REMPI spectrum in Figure 2. In the REMPI spectrum following 266 nm dissociation at a warmer temperature (210 K), j = 21 is a minor shoulder on the j = 20 peak, 11 whereas there is a pronounced peak in the REMPI spectrum at slightly shorter wavelengths than the j = 20 peak following 320 nm dissociation.This suggests the peak is primarily from the j = 42 P-branch transition which is not populated following 266 nm dissociation rather than the j = 21 S-branch transition.
The angular distributions of the rings corresponding to the R-branch transitions of j = 17 and j = 20 have 4-fold symmetry and the S-branch transitions have 2-fold as expected for a dissociation with v perpendicular to j.The slower fragments in the S-branch image of j = 17 have 2-fold symmetry.This is consistent with the assignment of the O-branch transition of j = 43, but the P-branch transition of j = 35 is expected to have 4-fold symmetry.It is likely the 2-fold symmetry from the Obranch and S-branch transitions are dominant.In the image of the R-branch transition of j = 17, both the R-branch transition of j = 17 and the P-branch transition of j = 39 are expected to have 4-fold symmetry as seen in the R-branch images in Figure 3, but the angular distribution of the slower fragments has 2fold symmetry.This suggests the presence of an overlapping, yet unassigned, O-or S-branch transition at this wavelength.Based on the assignments of nearby peaks by Morrill et al., 53 it is possible the O-branch transitions of j = 40−42 are in this energy range and would contribute to the observed 2-fold symmetry while still accounting for the observed velocity distribution because of the similarity in velocity for fragments in j = 39 and j = 40 states.
3.2.Photodissociation near 330 nm.3.2.1.O 2 (a 1 Δ g ) Rotational Distribution at 330 nm. Figure 6 shows the REMPI spectrum of O 2 (a 1 Δ g ) probed via the 1−0 band of the O 2 (d 1 Π g ←← a 1 Δ g ) transition in a one-color experiment near 330 nm.This spectrum supports a broad rotational distribution, consistent with conclusions based on the image  The Journal of Physical Chemistry A speed distributions for a 320 nm dissociation.The experimental spectrum is shown in black circles.The spectrum at shorter wavelengths is from a 2D-REMPI spectrum (vide infra), integrated over a narrow range of speeds corresponding to the O 2 (a 1 Δ g , v = 0) fragment (region A in Figure 7).The spectrum at longer wavelengths is a traditional 1D-REMPI spectrum in which the center of the detector was covered with a mask, and the total signal was collected with a PMT, without radial resolution.The O, P, R, and S branches are shown in maroon, green, blue, and purple, respectively, with the sum of the branches shown by the solid black line.The transition energies used in the fit were determined from the rotational levels of the O 2 (d 1 Π g , v = 1) state reported by O'Keeffe et al. 13 and fitting the rotational levels of O 2 (a 1 Δ g , v = 0) reported by Morrill et al. 53 to obtain spectroscopic constants, which were adjusted to better fit a previous REMPI spectrum of O 2 (a 1 Δ g , v = 0) following 266 nm dissociation. 33No data were collected at intermediate wavelengths.Given that the two spectra were collected independently, they have been scaled to best fit the simulation.The spectrum is congested and highly perturbed, and the intensity of specific transitions cannot be directly used to extract rotational populations.We have attempted to correct transition intensities by including scaling factors for each rotational level of the resonant d 1 Π g state that account for the perturbations by scaling all transitions that lead to the same final state equivalently based on fits to a known distribution

The Journal of Physical Chemistry A
(see the Supporting Information).Additionally, the highintensity peaks at short wavelengths are at wavelengths similar to peaks in the Huggins band absorption spectrum of O 3 , which may indicate that the increase in intensity is due to increased O 3 absorption rather than higher population in rotational states corresponding to the transitions at the highintensity wavelengths.The increase in the signal may also indicate that the rotational distribution of O 2 (a 1 Δ g ) and the branching ratio between the O 2 (a 1 Δ g ) and the O 2 (b 1 Σ g + ) may depend on whether the O 3 dissociation is on-or off-resonance with a Huggins band peak.Determining accurate populations is challenging despite our efforts, but the spectrum clearly implies a broad rotational distribution with a significant population in states ranging from j ∼ 15 to j ∼ 50, consistent with the analysis at 320 nm.In particular, signal intensity between 331 and 331.5 nm corresponds to transitions for j ≤ 25, whereas signal intensity between 326.5 and 328 nm corresponds to transitions for j ≥ 40.Speed distributions of images collected at wavelengths within the range of this spectrum are also consistent with the assigned rotational states.

O 2 (b 1 Σ g +
) Rotational Distribution at 330 nm.In addition to studies on the spin-forbidden dissociation via channel 4 producing O 2 (a 1 Δ g ) and O( 3 P) products, there have been previous studies on the O 2 (b 1 Σ g + ) fragment formed in channel 3. 13,34 The b 1 Σ g + state of O 2 is 5200 cm −1 higher in energy than the a 1 Δ g state 53 but with similar rotational constants. 34Because of symmetry restrictions, only even rotational states exist in the O 2 (b 1 Σ g + ) state.Previous studies on the O 2 (b 1 Σ g + ) fragment utilized REMPI schemes accessing the v = 1 or 2 state of the resonant d 1 Π g state, which are highly perturbed, making the rotational state distributions difficult to obtain.Fortuitously, 330 nm corresponds to the 4−0 band of the O 2 (d 1 Π g ←← b 1 Σ g + ) transition, which accesses the lowest unperturbed vibrational level of the d 1 Π g state, allowing the determination of accurate rotational state populations of the b 1 Σ g + state, which can be compared to the a 1 Δ g state populations.
Figure 7 shows a 2D-REMPI spectrum of O 2 in a one-color experiment following dissociation of O 3 near 330 nm.At each wavelength step in the scan, an image was collected, symmetrized, and reconstructed, and the reconstructed speed distribution was plotted as a function of wavelength to obtain the 2D spectrum.There are several structured bands clearly visible in Figure 7 at different speeds, which can be assigned to different electronic and vibrational states of O 2 based on the speed of the fragments and energy conservation.The fragments with the greatest speed (top of the figure) correspond to v = 0 of the O 2 (a 1 Δ g ) electronic state.The remaining signal is assigned to vibrational levels of the O 2 (b 1 Σ g + ) state, with the higher vibrational states appearing at slower speeds due to the increased internal energy.Narrow ranges of speed were integrated to obtain the 1D spectra shown on the right, each corresponding to a different electronic or vibrational state of O 2 .Region A is the spectrum included in Figure 6 and discussed previously.
Figure 8 shows an averaged image and corresponding speed distribution of a narrow slice of the 2D-REMPI, integrated between 327.970 and 328.145 nm.The speed distribution shows clear structure corresponding to O 2 (a 1 Δ g , v = 0) and O 2 (b 1 Σ g + , v = 0−4) products.The distribution has been fit with Gaussian distributions centered on the speeds expected for each vibrational and rotational state detected in the integrated wavelength region.The peak at 1700 m/s corresponds to v = 0 of O 2 (a 1 Δ g ).The peak at 1350 m/s corresponds to O 2 (b 1 Σ g + , v = 0), and O 2 (b 1 Σ g + , v = 1) appears as a shoulder on the v = 0 peak, indicating there is overlap between these two vibrational levels in the 1D rotational spectra shown in Figure 7.The other peaks in the speed distribution are consistent with the speeds expected for fragments in v = 2, 3, and The Gaussian distributions used to fit the speed distribution have increasing values of σ for the higher vibrational states to reflect the effect of similar energy distributions having broader speed distributions at low speeds.
The 1D rotational spectrum generated by integrating the 2D-REMPI over a narrow range of speeds can be fit to obtain rotational state populations for individual vibrational states.Figure 9 shows the 1D spectra of O 2 (b 1 Σ g + , v = 0).The REMPI spectrum was fit with a simulation using spectroscopic constants fit to transitions previously reported by O'Keeffe et al. for the b 1 Σ g + state 13 and constants from Morrill et al. for the d 1 Π g state. 53The simulation also includes two-photon line strengths from Bray and Hochstrasser. 54Linewidths in Figure 9 are based on previously reported j-dependent line width trends by Aardema et al., 31 slightly shifted to larger linewidths because of broadening as a result of additional laser power.The simulated P, R, and S branches in Figure 9 are shown in green, blue, and purple, respectively, and the sum of the  13 In comparison to the range of rotational states of O 2 (a 1 Δ g , v = 0) observed following both 320 and 330 nm dissociation of O 3 , the rotational distribution of the O 2 (b 1 Σ g + , v = 0) is much narrower, indicative of significantly different dynamics in the dissociation processes leading to each of the electronic channels.While there is clear evidence that the rotational distribution of O 2 (a 1 Δ g ) extends from at least j = 16 to j = 43 following dissociation at both 320 and 330 nm, there is only population in j = 24−40 of the b 1 Σ g + state.A narrow rotational distribution could be an indication of anisotropy in the potential or selectivity of molecules with a limited range of geometries that can transition from the B state of O 3 to the triplet states correlating with the O 2 (b 1 Σ g + ) and the O( 3 P) products, while molecules with a wider range of bond angles can transition from the B state to triplet states correlating with O 2 (a 1 Δ g ) and O( 3 P) products, leading to a broad rotational state distribution of O 2 (a 1 Δ g ).In the analysis of O( 3 P) images following spin-forbidden dissociation of O 3 by Ulrich et al., the authors assumed a single rotational temperature for each of the three O 2 electronic states that were produced with an O( 3 P) co-fragment. 6The difference in the width of the rotational distributions measured for O 2 (a 1 Δ g ) and O 2 (b 1 Σ g + ) indicates that the two distributions cannot be described by a single temperature.
The slower fragments in the 2D-REMPI are assigned to the 5−1, 6−2, 7−3, and 8−4 bands of the O 2 (d 1 Π g ←← b 1 Σ g + ) transition.The spacing of the peaks is consistent with the presence of only even rotational states expected for the O 2 (b 1 Σ g ) state, and the radial distribution is consistent with the expected speeds of the O 2 (b 1 Σ g + ) fragments in higher vibrational states, as seen in Figure 8.The lower vibrational levels (v = 0−2) of the O 2 (b 1 Σ g + ) state have been well characterized and rotational transitions have been assigned. 13,53Experimental rotational constants for v = 3 and v = 4 have not been reported to our knowledge but can be reasonably estimated from the lower vibrational levels.In the resonant O 2 (d 1 Π g ) state, however, rotational analysis has not been performed for v ≥ 5, and estimating rotational constants from the lower vibrational levels is not possible because v = 0− 3 are highly perturbed.Rotational constants were calculated using the BCONT program 55 which determines the eigenvalues for an assumed potential which was adjusted to fit the experimental spectra.We found that the vibrational levels of the d 1 Π g state needed to be shifted to lower energies than those predicted by the BCONT calculations and previously estimated by theory or from kinetic energy release spectra. 56EMPI spectra for the 5−1 and 8−4 bands of the O 2 (d 1 Π g ←← b 1 Σ g + ) transition are shown in Figure 11 as representative examples of fits to the rotational spectra for higher vibrational  ) are all probed simultaneously in the 2D-REMPI, the vibrational distribution can also be determined from the speed distribution of the spectrum.The 2D-REMPI was integrated from 327.620 to 328.870 nm to obtain the speed distribution of nearly the entire spectrum.
The wavelength range was chosen to maximize R-and Sbranch contributions and minimize P-branch contributions in O 2 (b 1 Σ g + , v = 0−3).The integrated speed distribution was fit with a Gaussian distribution for each vibrational level, centered at the speeds expected for a fragment in the rotational state in the middle of the rotational distribution for the given vibrational level.The Gaussian distributions were broader than the distributions in Figure 8   ) is similar to the distribution calculated for the O 2 (X 3 Σ g − ) fragment by Ulrich et al., which also peaks at v = 0 and decreases monotonically. 6lthough there is no evidence in the 2D-REMPI for higher vibrational states of O 2 (a 1 Δ g ), it is unclear whether this is due to low population or shifts in wavelength for the REMPI transitions of higher vibrational states.As with experiments at 320 nm, quantitative extraction of vector correlations was limited due to the single laser geometry in a one-color experiment and images were only collected with the laser vertically polarized.Additionally, isolation of individual rotational states was difficult due to the considerable overlap between the R-and S-branch transitions.Figure 14 shows the angular distributions of images collected at wavelengths corresponding to the S-branch transition of j = 34 and the R-branch transition of j = 32 of O 2 (b 1 Σ g + , v = 0).Typically analysis is performed on both branches of a single rotational state, but due to the highly overlapped R and S branches, nearby rotational states were chosen that had minimal contributions from the other rotational branch.Based on the fit to the REMPI spectrum in Figure 9, the S-branch transition for j = 34 has very little contribution from the R-branch transition for j = 40.The j = 32 R-branch transition has some overlap with the j = 26 S-branch transition, but the R-branch, j = 32 transition should be dominant based on the fit to the spectrum in Figure 9. Images were collected with a single, vertically polarized laser and reconstructed, and a narrow slice of the ring corresponding to O 2 (b 1 Σ g + , v = 0) was used for the angular distribution.The faint outer ring in the image is from O 2 (a 1 Δ g , v = 0), and moving to smaller radii, the next ring is from O 2 (b 1 Σ g + , v = 0).Because the b 1 Σ g + , v = 0 ring in the image of the j = 32 R-branch transition contains contribution from the S-branch transition of j = 26, the edge of the ring at smaller radii was used for the angular distribution because fragments in j = 32 should have slightly slower speeds than fragments in j = 26.The outer edge of the ring was used for j = 34, which should be faster than j = 40.The angular distributions were fit to eq 7 to obtain the anisotropy parameters in Table 2.The angular distribution has 2-fold symmetry in the S-branch and 4-fold symmetry in the R-branch as expected for a perpendicular v-j correlation.The β 2 parameter in the Sbranch image is similar to the β 2 parameters reported S-branch images of O 2 (a 1 Δ g ), but β 2 is lower in the R-branch image than O 2 (a 1 Δ g ).The value of β 4 is positive for the S-branch and

The Journal of Physical Chemistry A
negative for the R-branch, as seen in the ionization of the O 2 (a 1 Δ g ) fragment.
Using the R-and S-branch angular distributions to estimate bipolar moments gives β 0 2 (20) near 0.5 and β 0 0 (22) near −0.5, which is consistent with a parallel transition and perpendicular v-j correlation, as expected.The value of β 0 2 (20) is expected to be diminished from its limiting value of 1 due to the lifetime of the excited state, which Takahashi et al. estimate to be between 0.3 and 1.1 ps for excitation near 325 nm. 23This is also consistent with the image anisotropy parameters reported by Ulrich et al. for rings in the O( 3 P 2 ) images assigned to formation of an O 2 (b 1 Σ g + ) co-fragment, which primarily range from 0.55 to 1.98, corresponding to β 0 2 (20) values of 0.28 to 0.99. 6The image anisotropy parameters reported for the O 2 (a 1 Δ g ) fragments similarly range from 0.61 to 1.99.

CONCLUSIONS
The REMPI spectrum of O 2 (a 1 Δ g ) following 320 nm spinforbidden dissociation of O 3 probed via S-branch transitions of the O 2 (d 1 Π g , v = 2 ←← a 1 Δ g , v = 0) transition was reported, exhibiting greater intensity in peaks corresponding to odd rotational state transitions than even state transitions.While the observed alternation is opposite of that reported by Gunthardt et al. for the spin-allowed dissociation at 266 nm, 11 it is consistent with the coupling between the B state and 3 A′ and 3 A″ states correlating to spin-forbidden products calculated by Grebenshchikov and Rosenwaks. 12We are optimistic that in the future it will be possible to study predissociation via the 3 A′ and 3 A″ states independently.Images of odd and even rotational states at 320 nm have very similar angular distributions, indicating similar dissociation dynamics.The radial distributions of the images collected at 320 nm are multimodal, and the speeds of the fragments are consistent with the overlap between low j and high j peaks assigned by Morrill et al. 53 The radial distributions of these images indicate a broad rotational distribution of the O 2 (a 1 Δ g ) fragment, which is also observed following dissociation near 330 nm in the 1D-REMPI spectrum.In contrast, the 2D-REMPI spectrum at 330 nm indicates a much narrower rotational distribution of O 2 (b 1 Σ g + ) probed via the O 2 (d 1 Π g , v = 4 ←← b 1 Σ g + , v = 0) transition.There is evidence in the 2D-REMPI for the formation of higher vibrational states (v = 1−4) of O 2 (b 1 Σ g + ) as well, with rotational distributions similar to v = 0.The radial distribution of the 2D-REMPI was used to obtain the vibrational state distribution of the O 2 (b 1 Σ g + ) fragment, which is primarily formed in v = 0, with much less population in higher vibrational states.The difference in rotational distributions between the a 1 Δ g and b 1 Σ g + states of O 2 indicates different dynamics leading to these dissociation channels, possibly with higher selectivity of the O 3 bond angles in the channel forming O 2 (b 1 Σ g + ) + O( 3 P), leading to a narrower rotational distribution.
Future two-color experiments in the Huggins band would allow not only full vector correlation analysis but also studies on the wavelength dependence of the O 2 (a 1 Δ g ) and O 2 (b 1 Σ g + ) rotational state distributions.Dissociation at wavelengths corresponding to the excitation of different vibrational modes may result in different fragment rotational state distributions or differences in the branching ratio between O 2 electronic states, which are not distinguishable in the one-color experiments.
NO temperature calibration, a more detailed description of the Landau−Zener model used to estimate the relative probability of transitions from the B state to the 3A′ and 3A″ states, ion images and speed distributions for j = 17−20 in both the R and S branches, discussion of the scaling factors used in fitting the perturbed O 2 (d 1 Π g , v = 1 ←← a 1 Δ g , v = 0) REMPI spectrum, and the REMPI fits and rotational distributions for all O 2 (b 1 Σ g + ) vibrational states obtained in the 2D-REMPI spectrum (PDF)  The Journal of Physical Chemistry A

Figure 1 .
Figure 1.Potential energy curves calculated by Grebenshchikov and Rosenwaks. 12Solid black lines indicate 1 A′ states, including the X, B, and R states.Solid and dashed blue lines indicate 3 A′ and 3 A″ states, respectively, that cross the B state and lead to spin-forbidden products.

Figure 2 .
Figure 2. REMPI spectrum of the O 2 (a 1 Δ g ) fragment following the dissociation of jet-cooled O 3 probed via the O 2(d 1 Π g , v = 2 ←← a 1 Δ g , v = 0) transition.The bottom spectrum was collected following dissociation at 266 nm11 and the top spectrum near 320 nm in a onecolor experiment.S-branch transitions are indicated by the comb at the top, and the peak marked by an asterisk corresponds to the overlapping P-branch j = 42 transition.

Figure 3 .
Figure 3. Symmetrized images of O 2 (a 1 Δ g , v = 0) following dissociation of O 3 near 320 nm.A single, vertically polarized laser was used for both dissociation and probing the O 2 fragments at wavelengths corresponding to the S-and R-branch transitions of j = 19 and j = 20.The outer ring corresponds to spin-forbidden dissociation, and the innermost ring is energetically consistent with spin-allowed dissociation from vibrationally excited O 3 .The signal at intermediate radii is nonresonant.Angular distributions correspond to the outermost ring in the images.Black circles are the experimental angular distributions, and red lines are Legendre polynomials (eq 7) with the best-fit anisotropy parameters β 2 and β 4 reported in Table1.

Figure 4 .
Figure 4. Outer edge of the reconstructed images of O 2 (a 1 Δ g ) following 320 nm dissociation of O 3 are shown.Images taken at wavelengths corresponding to an S-branch transition of j = 20 (top left) and R-branch transition of j = 20 (top right) have a single outer ring.Images taken at wavelengths corresponding to the S-branch transition of j = 17 (bottom left) and the R-branch transition of j = 17 (bottom right) have multiple rings, indicative of overlapped rotational transitions.

Figure 5 .
Figure 5. Speed distributions of O 2 (a 1 Δ g ) extracted from the images shown in Figure 4. Distributions are shown for S-(left) and R-branch (right) images of j = 20 (top) and j = 17 (bottom).Images of both the S-and R-branch transitions of j = 20 are unimodal, indicating a single rotational state is observed at this wavelength.The image of the S-branch transition of j = 17 includes slow fragments attributed to the P-branch transition of j = 35 and the O-branch transition of j = 43, and the R-branch transition of j = 17 includes slow fragments assigned to the P-branch transition of j = 39.

Figure 6 .
Figure 6.REMPI spectrum of O 2 (a 1 Δ g ) following photodissociation of O 3 in one-color experiments near 330 nm, probed via the 1−0 band of the d 1 Π g ←← a 1 Δ g transition.Black circles indicate experimental data.The data at shorter wavelengths were collected in the 2D-REMPI in Figure7, and a narrow range of speeds was integrated to obtain the O 2 (a 1 Δ g , v = 0) spectrum.The longer-wavelength spectrum was collected in a one-color, 1D-REMPI experiment.The maroon, green, blue, and purple lines indicate the O, P, R, and S branches, respectively, and the solid black line is the sum of the branches.

Figure 7 .
Figure 7. 2D-REMPI spectrum of O 2 (b 1 Σ g + ) and O 2 (a 1 Δ g ) following the 330 nm dissociation of jet-cooled O 3 .The regions indicated by A−F were radially integrated to obtain the 1D spectra shown on the right.Region A is assigned to O 2 (a 1 Δ g , v = 0), and regions B−F are assigned to (b 1 Σ g + , v = 0−4) from top to bottom.

Figure 8 .
Figure 8. Image obtained from averaging all images collected in the 2D-REMPI spectrum in Figure7between 327.970 and 328.145 nm is shown above.This region was selected to include a single rotational peak from each vibrational level.The radial distribution of the averaged, reconstructed image is shown below.The speed distribution was fit with a sum of Gaussian distributions, with peaks corresponding to the speeds expected for the vibrational and rotational states included in the narrow-wavelength region.

Figure 9 .
Figure 9. 1D rotational spectrum of O 2 (b 1 Σ g + , v = 0) obtained by integrating a narrow range of speeds in the 2D-REMPI spectrum corresponding to region B in Figure 7.These wavelengths correspond to the 4−0 band of the O 2 (d 1 Π g ←← b 1 Σ g + ) transition.The experimental data are shown by black circles, and the P, R, and S branches of the simulated spectrum are shown in green, blue, and purple, respectively.The solid black line represents the sum of all of the simulated branches.

Figure 10 .
Figure 10.Rotational state distribution of O 2 (b 1 Σ g + , v = 0) fit to the REMPI spectrum shown in Figure 9.Only even rotational states of O 2 (b 1 Σ g + ) are permitted due to symmetry restrictions.
due to the increased range of speeds expected for a range of rotational states.The distributions were converted to energy, and the integrated areas of the fit Gaussian distributions were corrected for the Franck−Condon factors for each vibrational band of the O 2 (d 1 Π g ←← b 1 Σ g + ) transition to determine the population in each vibrational state.The resulting vibrational distribution is shown in Figure 13.The distribution peaks at v = 0 and decreases monotonically with increasing v, with very low populations at the higher vibrational states.Franck−Condon factors associated with the transitions increase with increasing initial vibrational level, which allows the detection of fragments in higher vibrational states despite their low population.The observed vibrational distribution is significantly different than the vibrational distribution reported by Ulrich et al. based on fits to the O( 3 P 2 ) speed distributions, which predicts a maximum population in v = 2 for their "full" model and v = 1

Figure 11 .
Figure 11.1D rotational spectra for the 5−1 (top) and 8−4 (bottom) bands of the O 2 (d 1 Π g ←← b 1 Σ g + ) transition following the dissociation of O 3 near 330 nm.The rotational spectra correspond to regions C and F of Figure 7.The experimental spectra are represented by black circles, and the simulated O, P, R, and S branches are shown in maroon, green, blue, and purple, respectively.The sum of the branches is represented by the solid black line.

Figure 12 .
Figure 12.Rotational state populations for O 2 (b 1 Σ g + , v = 1−4) following the dissociation of O 3 near 330 nm used to fit the rotational spectra in Figures 7 and 11.

Figure 13 .
Figure 13.Vibrational distribution of the O 2 (b 1 Σ g + ) fragment following 330 nm dissociation of O 3 , based on analysis of the speed distribution of the integrated 2D-REMPI spectrum and correcting for the Franck−Condon factor of each vibrational transition to the resonant d 1 Π g state.

Figure 14 .
Figure 14.Angular distributions of ion images of O 2 (b 1 Σ g + , v = 0) collected in a one-color experiment following the dissociation of O 3 .The wavelengths correspond to the S-branch transition of j = 34 (top) and the R-branch transition of j = 32 (bottom).The image corresponding to the S-branch transition of j = 34 is included.Images were reconstructed, and a thin slice of the ring corresponding to the O 2 (b 1 Σ g + , v = 0) ring was fit to eq 7 to obtain β 2 and β 4 image anisotropy parameters in Table 2. Black circles represent the experimental angular distribution, and red lines represent the fit to eq 7. The faint outer ring in the image corresponds to the ionic ring of O 2 (a 1 Δ g , v = 0), and the rings at smaller radii correspond to higher vibrational states of O 2 (b 1 Σ g + ).